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Hierarchical Additive Modeling of Nonlinear Association with Spatial Correlations-An Application to Relate Alcohol Outlet Density and Neighborhood Assault Rates

2008/02/04 by Qingzhao Yu, Yu, Qingzhao, Bin Li +6
Economics, Econometrics and Finance · Mathematics · Social Sciences · #Applications (stat.AP) #Crime Patterns and Interventions #FOS: Computer and information sciences #Methodology (stat.ME) #Spatial and Panel Data Analysis #Urban, Neighborhood, and Segregation Studies #stat.AP #stat.ME

paper · pdf · doi:10.48550/arxiv.0802.0450

26 pages, 4 figures, submitted

arxiv created 2008/02/04 · openalex publication_date 2008/02/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Previous studies have suggested a link between alcohol outlets and assaultive violence. In this paper, we explore the effects of alcohol availability on assault crimes at the census tract level over time. The statistical analysis is challenged by several features of the data: (1) the effects of possible covariates (for example, the alcohol outlet density of each census tract) on the assaultive crime rates may be complex; (2) the covariates may be highly correlated with each other; (3) there are a lot of missing inputs in the data; and (4) spatial correlations exist in the outcome assaultive crime rates. We propose a hierarchical additive model, where the nonlinear correlations and the complex interaction effects are modeled using the multiple additive regression trees (MART) and the spatial variances in the assaultive rates that cannot be explained by the specified covariates are smoothed trough the Conditional Autoregressive (CAR) model. We develop a two-stage algorithm that connect the non-parametric trees with CAR to look for important variables covariates associated with the assaultive crime rates, while taking account of the spatial correlations among adjacent census tracts. The proposed methods are applied to the Los Angeles assaultive data (1990-1999) and compared with traditional method.

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